Abstract

We present three new methods for modeling broad-bandwidth, nanosecond optical parametric oscillators in the plane-wave approximation. Each accounts for the group-velocity differences that determine the operating linewidth of unseeded optical parametric oscillators, and each allows the signal and the idler waves to develop from quantum noise. The first two methods are based on split-step integration methods in which nonlinear mixing and propagation are calculated separately on alternate steps. One method relies on Fourier transforming the fields between t and ω to handle propagation, with mixing integrated over a Δz step; the other transforms between z and kz in the propagation step, with mixing integrated over Δt. The third method is based on expansion of the three optical fields in terms of their respective longitudinal empty cavity modes, taking into account the cavity boundary conditions. Equations describing the time development of the mode amplitudes are solved to yield the time dependence of the three output fields. These models exclude diffraction and group-velocity dispersion but can be readily extended to include them.

© 1999 Optical Society of America

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References

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  1. A. V. Smith, W. J. Alford, T. D. Raymond, and M. S. Bowers, “Comparison of a numerical model with measured performance of a seeded, nanosecond KTP optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2253–2267 (1995).
    [CrossRef]
  2. D. J. Armstrong and A. V. Smith, “Tendency of nanosecond optical parametric oscillators to produce purely phase-modulated light,” Opt. Lett. 21, 1634–1636 (1996).
    [CrossRef] [PubMed]
  3. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  4. E. S. Cassedy and M. Jain, “A theoretical study of injection tuning of optical parametric oscillators,” IEEE J. Quantum Electron. QE-15, 1290–1301 (1979).
    [CrossRef]
  5. Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
    [CrossRef]
  6. T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
    [CrossRef]
  7. K.-J. Boller and T. Schroder, “Demonstration of broadband intracavity spectroscopy in a pulsed optical parametric oscillator made of β-barium borate,” J. Opt. Soc. Am. B 10, 1778–1784 (1993).
    [CrossRef]
  8. A. Fix and R. Wallenstein, “Spectral properties of pulsed nanosecond optical parametric oscillators: experimental investigation and numerical analysis,” J. Opt. Soc. Am. B 13, 2484–2497 (1996).
    [CrossRef]
  9. G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” Proc. SPIE 3685, 86–97 (1999); G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16, 117–127 (1999).
    [CrossRef]
  10. A. Yariv and W. H. Louisell, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
    [CrossRef]
  11. T. Debuisschert, “Nanosecond optical parametric oscillators,” Quantum Semiclassic. Opt. 9, 209–219 (1997).
    [CrossRef]
  12. K. D. Shaw, “Spatio-temporal evolution of the intra-cavity fields in a pulsed doubly resonant optical parametric oscillator,” Opt. Commun. 144, 134–160 (1997).
    [CrossRef]
  13. H. J. Bakker, P. C. M. Planken, and H. G. Muller, “Numerical calculation of optical frequency-conversion processes: a new approach,” J. Opt. Soc. Am. B 6, 1665–1672 (1989).
    [CrossRef]
  14. M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
    [CrossRef]
  15. R. Danielius, A. Dubietis, A. Piskarskas, G. Valiulis, and A. Varanavicius, “Generation of compressed 600–720-nm tunable femtosecond pulses by transient frequency mixing in a β-barium borate crystal,” Opt. Lett. 21, 216–218 (1996).
    [CrossRef] [PubMed]
  16. R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
    [CrossRef]
  17. S. Fournier, R. Lopez-Martens, C. Le Blanc, E. Baubeau, and F. Salin, “Solitonlike pulse shortening in a femtosecond parametric amplifier,” Opt. Lett. 23, 627–629 (1998).
    [CrossRef]
  18. D. Kim and G.-Y. Xiao, “Distortion of a chirped short pulse in type II second-harmonic generation,” J. Opt. Soc. Am. B 15, 570–576 (1998).
    [CrossRef]
  19. P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency conversion modeling with spatially and temporally varying beams,” Proc. SPIE 2633, 230–241 (1997).
    [CrossRef]
  20. T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
    [CrossRef]
  21. T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
    [CrossRef]
  22. G. M. Gale, M. Cavallari, and F. Hache, “Femtosecond visible optical parametric oscillator,” J. Opt. Soc. Am. B 15, 702–714 (1998).
    [CrossRef]
  23. B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 67, 537–544 (1998).
    [CrossRef]
  24. M. S. Bowers and S. E. Moody, “Cavity equations for a laser with an externally injected signal,” J. Opt. Soc. Am. B 11, 2266–2275 (1994).
    [CrossRef]
  25. A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49–57 (1995).
    [CrossRef]
  26. SNLO nonlinear optics software is available from A. V. Smith, Dept. 1128, Sandia National Laboratories, 87185–1423, or it may be downloaded from www site http://www.sandia.gov/imrl/XWEB1128/xxtal.htm. Methods 1 and 2 are run by the Run and Movie buttons of function PW-OPO-BB, respectively.

1998 (5)

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

S. Fournier, R. Lopez-Martens, C. Le Blanc, E. Baubeau, and F. Salin, “Solitonlike pulse shortening in a femtosecond parametric amplifier,” Opt. Lett. 23, 627–629 (1998).
[CrossRef]

D. Kim and G.-Y. Xiao, “Distortion of a chirped short pulse in type II second-harmonic generation,” J. Opt. Soc. Am. B 15, 570–576 (1998).
[CrossRef]

G. M. Gale, M. Cavallari, and F. Hache, “Femtosecond visible optical parametric oscillator,” J. Opt. Soc. Am. B 15, 702–714 (1998).
[CrossRef]

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 67, 537–544 (1998).
[CrossRef]

1997 (3)

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency conversion modeling with spatially and temporally varying beams,” Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

T. Debuisschert, “Nanosecond optical parametric oscillators,” Quantum Semiclassic. Opt. 9, 209–219 (1997).
[CrossRef]

K. D. Shaw, “Spatio-temporal evolution of the intra-cavity fields in a pulsed doubly resonant optical parametric oscillator,” Opt. Commun. 144, 134–160 (1997).
[CrossRef]

1996 (3)

1995 (5)

A. V. Smith, W. J. Alford, T. D. Raymond, and M. S. Bowers, “Comparison of a numerical model with measured performance of a seeded, nanosecond KTP optical parametric oscillator,” J. Opt. Soc. Am. B 12, 2253–2267 (1995).
[CrossRef]

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

A. V. Smith and M. S. Bowers, “Phase distortions in sum- and difference-frequency mixing in crystals,” J. Opt. Soc. Am. B 12, 49–57 (1995).
[CrossRef]

1994 (2)

M. S. Bowers and S. E. Moody, “Cavity equations for a laser with an externally injected signal,” J. Opt. Soc. Am. B 11, 2266–2275 (1994).
[CrossRef]

T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
[CrossRef]

1993 (1)

1989 (1)

1979 (1)

E. S. Cassedy and M. Jain, “A theoretical study of injection tuning of optical parametric oscillators,” IEEE J. Quantum Electron. QE-15, 1290–1301 (1979).
[CrossRef]

1977 (1)

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

1966 (1)

A. Yariv and W. H. Louisell, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

Alford, W. J.

Armstrong, D. J.

Auerbach, J. M.

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency conversion modeling with spatially and temporally varying beams,” Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

Bakker, H. J.

Baubeau, E.

Boller, K.-J.

T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
[CrossRef]

K.-J. Boller and T. Schroder, “Demonstration of broadband intracavity spectroscopy in a pulsed optical parametric oscillator made of β-barium borate,” J. Opt. Soc. Am. B 10, 1778–1784 (1993).
[CrossRef]

Bowers, M. S.

Cassedy, E. S.

E. S. Cassedy and M. Jain, “A theoretical study of injection tuning of optical parametric oscillators,” IEEE J. Quantum Electron. QE-15, 1290–1301 (1979).
[CrossRef]

Cavallari, M.

G. M. Gale, M. Cavallari, and F. Hache, “Femtosecond visible optical parametric oscillator,” J. Opt. Soc. Am. B 15, 702–714 (1998).
[CrossRef]

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

Danelyus, R.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Danielius, R.

Debuisschert, T.

T. Debuisschert, “Nanosecond optical parametric oscillators,” Quantum Semiclassic. Opt. 9, 209–219 (1997).
[CrossRef]

Deng, D.

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

Dikchyus, G.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Dubietis, A.

Eimerl, D.

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency conversion modeling with spatially and temporally varying beams,” Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

Fix, A.

A. Fix and R. Wallenstein, “Spectral properties of pulsed nanosecond optical parametric oscillators: experimental investigation and numerical analysis,” J. Opt. Soc. Am. B 13, 2484–2497 (1996).
[CrossRef]

T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
[CrossRef]

Fournier, S.

Gale, G. M.

G. M. Gale, M. Cavallari, and F. Hache, “Femtosecond visible optical parametric oscillator,” J. Opt. Soc. Am. B 15, 702–714 (1998).
[CrossRef]

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

Hache, F.

G. M. Gale, M. Cavallari, and F. Hache, “Femtosecond visible optical parametric oscillator,” J. Opt. Soc. Am. B 15, 702–714 (1998).
[CrossRef]

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

Jain, M.

E. S. Cassedy and M. Jain, “A theoretical study of injection tuning of optical parametric oscillators,” IEEE J. Quantum Electron. QE-15, 1290–1301 (1979).
[CrossRef]

Kabelka, V.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Kim, D.

Kong, Y.

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

Le Blanc, C.

Lopez-Martens, R.

Louisell, W. H.

A. Yariv and W. H. Louisell, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

Milonni, P. W.

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency conversion modeling with spatially and temporally varying beams,” Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

Moody, S. E.

Muller, H. G.

Nebel, A.

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 67, 537–544 (1998).
[CrossRef]

Nishikawa, T.

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[CrossRef]

Pavlov, L. I.

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

Piskarskas, A.

R. Danielius, A. Dubietis, A. Piskarskas, G. Valiulis, and A. Varanavicius, “Generation of compressed 600–720-nm tunable femtosecond pulses by transient frequency mixing in a β-barium borate crystal,” Opt. Lett. 21, 216–218 (1996).
[CrossRef] [PubMed]

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Planken, P. C. M.

Raymond, T. D.

Rousseau, E.

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

Ruffing, B.

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 67, 537–544 (1998).
[CrossRef]

Salin, F.

Schroder, T.

T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
[CrossRef]

K.-J. Boller and T. Schroder, “Demonstration of broadband intracavity spectroscopy in a pulsed optical parametric oscillator made of β-barium borate,” J. Opt. Soc. Am. B 10, 1778–1784 (1993).
[CrossRef]

Shaw, K. D.

K. D. Shaw, “Spatio-temporal evolution of the intra-cavity fields in a pulsed doubly resonant optical parametric oscillator,” Opt. Commun. 144, 134–160 (1997).
[CrossRef]

Smith, A. V.

Stabinis, A.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Uesugi, N.

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

Valiulis, G.

Varanavicius, A.

Wallenstein, R.

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 67, 537–544 (1998).
[CrossRef]

A. Fix and R. Wallenstein, “Spectral properties of pulsed nanosecond optical parametric oscillators: experimental investigation and numerical analysis,” J. Opt. Soc. Am. B 13, 2484–2497 (1996).
[CrossRef]

T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
[CrossRef]

Wu, L.

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

Xiao, G.-Y.

Xu, Z.

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

Yariv, A.

A. Yariv and W. H. Louisell, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

Yasevichyute, Ya.

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Zhou, Y.

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

Zhu, X.

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (2)

T. Schroder, K.-J. Boller, A. Fix, and R. Wallenstein, “Spectral properties and numerical modeling of a critically phase-matched nanosecond LiB3O5 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 58, 425–438 (1994).
[CrossRef]

B. Ruffing, A. Nebel, and R. Wallenstein, “All-solid-state cw mode-locked picosecond KTiOAsO4 optical parametric oscillator,” Appl. Phys. B: Photophys. Laser Chem. 67, 537–544 (1998).
[CrossRef]

IEEE J. Quantum Electron. (3)

E. S. Cassedy and M. Jain, “A theoretical study of injection tuning of optical parametric oscillators,” IEEE J. Quantum Electron. QE-15, 1290–1301 (1979).
[CrossRef]

Y. Kong, Z. Xu, Y. Zhou, D. Deng, X. Zhu, and L. Wu, “The compound cavity optical parametric oscillator: theory and experiment,” IEEE J. Quantum Electron. 34, 439–446 (1998).
[CrossRef]

A. Yariv and W. H. Louisell, “Theory of the optical parametric oscillator,” IEEE J. Quantum Electron. QE-2, 418–424 (1966).
[CrossRef]

J. Appl. Phys. (2)

T. Nishikawa and N. Uesugi, “Effects of walk-off and group velocity difference on the optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 77, 4941–4947 (1995).
[CrossRef]

T. Nishikawa and N. Uesugi, “Transverse beam profiles on traveling-wave optical parametric generation in KTiOPO4 crystals,” J. Appl. Phys. 78, 6361–6366 (1995).
[CrossRef]

J. Opt. Soc. Am. B (8)

Opt. Commun. (2)

M. Cavallari, G. M. Gale, F. Hache, L. I. Pavlov, and E. Rousseau, “Mid infra-red femtosecond pulse generation by wave-mixing: numerical simulation an experiment,” Opt. Commun. 114, 329–332 (1995).
[CrossRef]

K. D. Shaw, “Spatio-temporal evolution of the intra-cavity fields in a pulsed doubly resonant optical parametric oscillator,” Opt. Commun. 144, 134–160 (1997).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (1)

P. W. Milonni, J. M. Auerbach, and D. Eimerl, “Frequency conversion modeling with spatially and temporally varying beams,” Proc. SPIE 2633, 230–241 (1997).
[CrossRef]

Quantum Semiclassic. Opt. (1)

T. Debuisschert, “Nanosecond optical parametric oscillators,” Quantum Semiclassic. Opt. 9, 209–219 (1997).
[CrossRef]

Sov. J. Quantum Electron. (1)

R. Danelyus, G. Dikchyus, V. Kabelka, A. Piskarskas, A. Stabinis, and Ya. Yasevichyute, “Parametric excitation of light in the picosecond range,” Sov. J. Quantum Electron. 7, 1360–1368 (1977).
[CrossRef]

Other (3)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

G. Arisholm, “Advanced numerical simulation models for second-order nonlinear interactions,” Proc. SPIE 3685, 86–97 (1999); G. Arisholm, “Quantum noise initiation and macroscopic fluctuations in optical parametric oscillators,” J. Opt. Soc. Am. B 16, 117–127 (1999).
[CrossRef]

SNLO nonlinear optics software is available from A. V. Smith, Dept. 1128, Sandia National Laboratories, 87185–1423, or it may be downloaded from www site http://www.sandia.gov/imrl/XWEB1128/xxtal.htm. Methods 1 and 2 are run by the Run and Movie buttons of function PW-OPO-BB, respectively.

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Figures (9)

Fig. 1
Fig. 1

Diagram of the optical parametric oscillators modeled in this paper. The reflectivities of mirrors M2 and M3 are 1.0 for all three waves. Mirror M1 reflectivities and other parameters are given in Tables 1 and 2.

Fig. 2
Fig. 2

Example of OPO model gridding for split-step method 1. The pulses are gridded in time at each z point.

Fig. 3
Fig. 3

Example of OPO model gridding for split-step method 2. The z grids outside the crystal are spaced by Δz=cΔt; that inside the crystal is spaced by Δz=vmΔt, where vm is the fastest of the three group velocities.

Fig. 4
Fig. 4

Signal spectra for OPO of Table 2 pumped at twice threshold. The top two traces are for individual pulses with different start-up noise. The bottom trace is the average of ten pulses with fluctuating start-up noise. The averaged spectral width is ∼2.5 cm-1 compared with the crystal acceptance bandwidth of 8 cm-1.

Fig. 5
Fig. 5

Signal spectra for OPO of Table 2 pumped at twice threshold. The cw seed power incident on the input mirror is varied from 0 to 100 nW with the same start-up noise for each pulse. The spectra are normalized, so the sum of the energy in all modes is unity. Note the scale changes between the graphs.

Fig. 6
Fig. 6

Time profiles of the signal wave for the OPO of Table 1 with pump pulse fluences near threshold, twice threshold, and four times threshold. The pump pulse is centered a time zero and has a 7-ns width (FWHM).

Fig. 7
Fig. 7

Time profile of the signal wave of the OPO of Table 2 pumped at twice threshold. One half of a cavity round trip is displayed starting about midway through the signal pulse.

Fig. 8
Fig. 8

Computed spectrum of the depleted pump wave for the OPO of Table 2 pumped at twice threshold.

Fig. 9
Fig. 9

Measured spectra of the depleted pump wave for unseeded (middle trace) and seeded (bottom trace) OPO of Table 2. The top trace is a reference trace with the signal path blocked inside the OPO cavity. Each sideband is the overlap of sidebands from several etalon orders. The etalon free spectral range is 45.4 GHz, and the OPO cavity free spectral range is 4.1 GHz. The peaks at +2 and +14 GHz are measurement artifacts.

Tables (2)

Tables Icon

Table 1 Parameters of Example OPO

Tables Icon

Table 2 Parameters of KTP Ring OPO

Equations (33)

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Es(t, z)=12{s(t, z)exp[-i(ωst-ksz)]+s*(t, z)exp[i(ωst-ksz)]},
jout(t, z=0)=1-Rjjcirc(t, z=L)exp(iϕj)-Rjjin(t, z=0),
jcirc(t, z=0)=1-Rjjin(t, z=0)+Rjjcirc(t, z=L)exp(iϕj),
j(t, z=zin)=1-Rjinnjjcirc(t, z=zin),
jcirc(t, z=zout)=(1-Rjout)njj(t, z=zout).
z+1vst+iαs2t2s(t, z)=iωsdeffnscp(t, z)i*(t, z)exp(iΔkz)Ps(t, z),
z+1vit+iαi2t2i(t, z)=iωideffnicp(t, z)s*(t, z)exp(iΔkz)Pi(t, z),
z+1vpt+iαp2t2p(t, z)=iωpdeffnpci(t, z)s(t, z)exp(-iΔkz)Pp(t, z),
Δk=kp-ks-ki,
ωp=ωs+ωi.
1v=nc+ωcdndω=dkdω.
τjk=Lc1vj-1vk,
z=z,
t=t-z/vm,
z+1vj-1vmtj(t, z)=0.
z+iΔωj1vj-1vmj(Δωj, z)=0,
j(Δωj, z)=-j(t, z)exp(iΔωjt)dt,
zj(t, z)=Pj(t, z)
z=z-vmt,
t=t,
(vj-vm)z+tj(t, z)=0.
i(vj-vm)Δkz+tj(t, Δkz)=0.
tj(t, z)=vjPj(t, z)
j(t, z)=Aj(t, z)uj(z)γj exp-zLln(γj)+jinj(t, z).
duj(z)dz=0
Rj exp(iωjL/c)uj(L)=γjuj(0).
γj=Rj1-Rjout1-Rjin exp(iϕj),
jinj(t, 0)=1-Rjjin(t)+Rjjinj(t, L)exp(iϕj).
z+1vjt-1Lln γjAj(t, z)=Pj(t, z)γjuj(z)exp(-z ln γj/L)
Aj(t, 0)=Aj(t, L)
Aj(t, z)=qAqj(t)exp(-i2πqz/L),
dAqj(t)dt=1LqVq,qjAqj(t)(ln γj+i2πq)+1L0Ldzvj(z)Pj(t, z)γjuj(z)×expzLln γj+i2πqzL,
Vq,qj=1L0Ldzvj(z)expi2π(q-q)zL.

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